where \(k_t\)  is a sequence such that \(\sum _t k_t = \infty \)  and \(\sum _t k_t^2 < \infty \) . When the \(\eta _t\)  sequence effectively converges, the limit is the suggested learning rate \(\hat{\eta }\) . This is what [1]} refer to as the generalized posterior calibration (GPC) algorithm. Like SafeBayes, it is relatively expensive computationally—these algorithms require posterior computations for multiple learning rates and data sets—but the benefit is having a posterior distribution with meaningful spread, even in finite samples.
